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C₂×#17674 #6343796

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

(1,2);(3,4,7,11,8,12,6,10)(5,13,14,18,15,9,16,17)(19,20)(21,28,30,33)(22,31)(23,26)(24,27)(25,29,34,32);(3,5)(4,9)(6,14)(7,16)(8,15)(10,17)(11,18)(12,13)(19,21)(20,25)(22,29)(23,32)(24,30)(26,33)(27,34)(28,31);(3,6,8,7)(4,10,12,11)(5,14,15,16)(9,17,13,18)(19,22,24,23)(20,26,27,31)(21,29,30,32)(25,33,34,28);(3,6,8,7)(4,11,12,10)(5,14,15,16)(9,18,13,17)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250992);